Observations of the soft X-ray background with Chandra and XMM for example yield the line-of-
sight integral of the emission. A significant part of it is local being du to the glow of the heliosphere
and geocorona. Whereas the time-varying X-ray contribution can be accounted for via
phenomenological methods, the persistent emission from the outer heliosphere must be modeled
numerically. The heliospheric soft X-ray emission is due to charge-exchange collisions between solar
wind ions and neutrals from the local ISM. The overall appearance of the X-ray glow is determined by
the interaction of the solar wind and the local ISM. Using numerical models for the outer heliosphere,
we traced the charge-exchange evolution of 45 different solar wind ions along the streamlines and
computed the X-ray emissivity, surface brightness and spectral maps. Interestingly, the evolution of
the solar wind ion-composition and the accompanying spectral changes across the heliosheath can
serve as a diagnostic for the solar wind-LISM interaction. Similar models can be made for
astrospheres of nearby Sun-like stars.